Rudolf Müller - Maastricht University

Combinatorial auction design - algorithms and economics

Abstract:
Multi-item auctions are auctions in which an auctioneer wants to
sell a set of indivisible items. They have gained increasing scientific
interest in economics, computer science, and recently in combinatorial
optimization. This is due to applications in electronic marketplaces, and
market-based mechanisms for resource allocation problems in production and
transportation. A combinatorial auction is a multi-item auction
in which
bidders can make bids for subsets of items. Combinatorial auctions have
superior economic properties if bidders have valuations for subsets of items
that differ from the sum of valuations of items in the subset. For example, a
customer of an online auction might want to purchase a CD player and an
amplifier. Both items complement each other. Participating in separate auctions
leaves her with the risk to win only one of the two items, a combinatorial
auction can omit this.

The lecture investigates combinatorial auctions from an economic and a
combinatorial optimization perspective. It describes the economic properties of
the Vickrey-Clarke-Groves mechanism, and the combinatorial optimization
problems that have to be solved in order to make this mechanism applicable in
practice. It shows how a class of primal-dual algorithms for set packing
relates to combinatorial auction design. For the special case of single-item
auctions, it is shown that primal-dual algorithms define computationally
efficient auctions that fulfill at the same time nice economic properties. The
lecture is based on joined work with Andreas S. Schulz.